Mass signals in mass spectrometers are generally measured as a function of the scan time or the time of flight. The times of the appearance of these signals are then converted into masses via a so-called calibration curve. The accuracy of the mass determination is not always satisfactory, it is dependent on the type of mass spectrometer and the ionization method being used. In this context, “accuracy” is defined as the width of the error distribution. “Error” is the deviation between the measured mass value and the true mass value. The scattering of mass values around the true value is referred to here as the error distribution. One measure of the error distribution is the “standard deviation”, but a clearer way of expressing this is the “error distribution width” measured as the full width of the error distribution at half-maximum (sometimes abbreviated to FWHM).
Mass spectrometers can only ever measure the “mass per elementary charge” m/z of an ion. It is therefore crucial that the charge is determined in a known way and corrected for in the mass determination under discussion here. There are so-called deconvolution methods known in mass spectrometry to calculate true mass spectra from m/z-spectra containing ions with multiple elementary charges, taking into account the multiple numbers of protons in multiply charged ions.
From the work of Mathias Mann, it is known that peptides and proteins cannot assume all possible fractional mass values, but concentrate themselves in narrow distributions around average mass values. These average mass values are 1.00048 atomic mass units (amu) apart and have a distribution width of approximately 0.2 mass units (Proceedings of the 43rd ASMS Conference on Mass Spectroscopy and Allied Topics, Atlanta, Ga., USA, 1995, Page 639). A “straight line of best fit” on which the average values of the distributions lie can be easily constructed from these distances. The average values represent the “most probable” mass values for peptide ions.
In appropriate mass spectrometers, this knowledge can be used for recalibration and can therefore be used to improve the mass determination. A precondition for this is that the mass spectrometer has a “smooth” calibration curve which is described well by a mathematical function such as a low-order polynomial. If systematic errors of the mass values appear under these circumstances and can be attributed to the ionization process, affecting all ions to an equal extent, recalibration can be used. An example of this is MALDI time-of-flight mass spectrometers where there are fluctuations in the initial energy of the ions caused by the ionization by the matrix-assisted laser-desorption (MALDI) process, in spite of the spectrometers having very smooth calibration curves. The fluctuations in initial energy systematically leave their impression on the mass determinations.
For this recalibration, the measured masses are first replaced by the most probable masses arising from the above distances (i.e. from the “line of best fit”) and a mathematical best-fit curve is plotted through these most probable masses and associated scan times according to a method such as the method of minimum quadratic deviation. In other words, the most probable mass values are treated as a large number of reference masses. The curve therefore represents a most-probable calibration curve and the measured masses are “recalibrated” using the most-probable calibration curve just constructed. The recalibration procedure eliminates the systematic errors which occur in the mass spectrometer.
In some recent work the masses of peptides and their distribution were analyzed more accurately than was possible with the theoretical precalculation of M. Mann. By virtual tryptic digestion of all digestion peptides from a large protein sequence database, it is possible to determine the average masses of all the digestion peptides produced by the enzyme trypsin and determine their distribution widths. This produces average masses with an averaged mass separation of 1.0045475 atomic mass units in each case with a distribution width of only about 0.1 mass units for a mass of 1000 (S. Gay, P-A. Binz, D. F. Hochstrasser and R. D. Appel, Electrophoresis 1999, 20, 3527-3534). FIG. 1 shows typical distributions ranging over two mass units. The inclination of the “straight line of best fit” with this calculation method is slightly different to the one given by Mann.
On closer inspection of the individual average masses of peptides and proteins, it can be seen that the average mass values deviate characteristically from the “straight lines of best fit”. As shown in FIG. 2 for the mass range from about 300 to 1400 atomic mass units, the deviations show a period of 14 mass units; in this case, the amplitude of deviation of this period decreases from about 60 millimass units (peak-peak) toward the higher masses and disappears altogether at about 1400 mass units. Beyond 3000 mass units, statistical deviations appear in the individual average mass values which increase in size toward the higher masses but do not have any recognizable periodicity, as seen in FIG. 3.
These individual deviations in the peptide masses can be used for a more accurate recalibration by using the individual average values for the mass numbers instead of using the value for the “straight lines of best fit” for the recalibration process. (In this context, the “mass number” is the nucleon number, i.e. the number of protons and neutrons counted together).
In a similar way, average values for the masses can be calculated for other classes of biopolymers by combinatorial analysis or by virtual digestion of sequences in databases. Such classes may include glycoproteins, lipoproteins, saccharines or DNA etc. The proteins from mammals and the proteins from bacteria can be regarded as two separate classes since the proteins from bacteria have a different proportion of the various amino acids and therefore show slightly different average mass values. Some of the biopolymers of certain selected classes have distribution ranges around the individual average mass values which are even narrower than those of the proteins, and are therefore even more accurate.
However, the methods for recalibration described cannot be used if the mass spectrometer yields statistical or pseudostatistical error distributions in the mass determination. “Pseudostatistical error distributions” in this context means those mass errors which, although they can be reproduced from scan to scan, always show relatively large differences between the measured and true masses. These differences deviate positively and negatively along the mass scale and therefore cannot be represented by a smooth calibration curve.
Mass spectrometers which show this behavior include, for example, high-frequency ion trap mass spectrometers, where the pseudostatistical deviations may be caused by tiny fluctuations in the control of the high-frequency scan. Other causes may also be the effects of the space charge and the order structure within the ion cloud on scanning behavior and therefore the mass determination.
However, there are other mass spectrometers which also show the phenomenon of statistical or pseudostatistical mass deviation.